Fictitious domain methods using cut elements: III. A stabilized Nitsche method for Stokes’ problem

Erik Burman; Peter Hansbo

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2014)

  • Volume: 48, Issue: 3, page 859-874
  • ISSN: 0764-583X

Abstract

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We extend our results on fictitious domain methods for Poisson’s problem to the case of incompressible elasticity, or Stokes’ problem. The mesh is not fitted to the domain boundary. Instead boundary conditions are imposed using a stabilized Nitsche type approach. Control of the non-physical degrees of freedom, i.e., those outside the physical domain, is obtained thanks to a ghost penalty term for both velocities and pressures. Both inf-sup stable and stabilized velocity pressure pairs are considered.

How to cite

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Burman, Erik, and Hansbo, Peter. "Fictitious domain methods using cut elements: III. A stabilized Nitsche method for Stokes’ problem." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.3 (2014): 859-874. <http://eudml.org/doc/273126>.

@article{Burman2014,
abstract = {We extend our results on fictitious domain methods for Poisson’s problem to the case of incompressible elasticity, or Stokes’ problem. The mesh is not fitted to the domain boundary. Instead boundary conditions are imposed using a stabilized Nitsche type approach. Control of the non-physical degrees of freedom, i.e., those outside the physical domain, is obtained thanks to a ghost penalty term for both velocities and pressures. Both inf-sup stable and stabilized velocity pressure pairs are considered.},
author = {Burman, Erik, Hansbo, Peter},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {finite element methods; stabilized methods; penalty methods; Stokes’ problem; fictitious domain; Stokes' problem},
language = {eng},
number = {3},
pages = {859-874},
publisher = {EDP-Sciences},
title = {Fictitious domain methods using cut elements: III. A stabilized Nitsche method for Stokes’ problem},
url = {http://eudml.org/doc/273126},
volume = {48},
year = {2014},
}

TY - JOUR
AU - Burman, Erik
AU - Hansbo, Peter
TI - Fictitious domain methods using cut elements: III. A stabilized Nitsche method for Stokes’ problem
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2014
PB - EDP-Sciences
VL - 48
IS - 3
SP - 859
EP - 874
AB - We extend our results on fictitious domain methods for Poisson’s problem to the case of incompressible elasticity, or Stokes’ problem. The mesh is not fitted to the domain boundary. Instead boundary conditions are imposed using a stabilized Nitsche type approach. Control of the non-physical degrees of freedom, i.e., those outside the physical domain, is obtained thanks to a ghost penalty term for both velocities and pressures. Both inf-sup stable and stabilized velocity pressure pairs are considered.
LA - eng
KW - finite element methods; stabilized methods; penalty methods; Stokes’ problem; fictitious domain; Stokes' problem
UR - http://eudml.org/doc/273126
ER -

References

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